Question

Write an equation and solve. Jeff can wash and wax his car in 3 hours, but his dad can do it in only 2 hours. How long will it take the two of them to wash and wax together?

108

likes
539 views

Answer to a math question Write an equation and solve. Jeff can wash and wax his car in 3 hours, but his dad can do it in only 2 hours. How long will it take the two of them to wash and wax together?

Expert avatar
Cristian
4.7
119 Answers
Let's denote the time it takes for Jeff to wash and wax the car as x hours and the time it takes for his dad to wash and wax the car as y hours.

Jeff can do the job in 3 hours, so his work rate is \frac{1}{3} of the car per hour.
Similarly, Jeff's dad can do the job in 2 hours, so his work rate is \frac{1}{2} of the car per hour.

When they work together, their work rates are combined, so the equation becomes:
\frac{1}{3} + \frac{1}{2} = \frac{1}{x} + \frac{1}{y}

To solve for x and y , we notice that Jeff and his dad are working on the same job, the time taken when working together is the same, so:
\frac{1}{x} + \frac{1}{y} = \frac{1}{3} + \frac{1}{2} = \frac{5}{6}

Now, we need to find the time for both of them to complete the job together, which is the reciprocal of the combined work rate:
x = y = \frac{1}{\frac{5}{6}} = \frac{6}{5} \text{ hours}

Therefore, it will take Jeff and his dad \frac{6}{5} hours to wash and wax the car together.

\boxed{\frac{6}{5}\text{ or 1.2 hours}}

Frequently asked questions (FAQs)
What is the common radian measure for an angle of 90 degrees?
+
What is the probability of rolling a pair of dice and getting a sum greater than 9?
+
Question: Simplify (3^2 * 3^4) / (3^3 - 3^2)
+
New questions in Mathematics
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
If you have a bag with 18 white balls and 2 black balls. What is the probability of drawing a white ball? And extracting a black one?
5/8 x 64
Let I ⊂ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≤ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)
Consider numbers from 1 to 2023. We want to delete 3 consecutive, so that the avarage of the left numbers is a whole number. How do we do that
Answer the following questions regarding the expression below. 0.1 (a) Write the number as a fraction.
Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll? Draw the diagram
Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)
prove that if n odd integer then n^2+5 is even
-3(-4x+5)=-6(7x-8)+9-10x
(2m+3)(4m+3)=0
-1%2F2x-4%3D18
3%2B2
A,B,C and D are the corners of a rectangular building. Find the lengths the diagonals if AB measures 38' - 9" and AD measures 56' - 3"
The blood types of individuals in society are as follows: A: 30%, B: 25%, AB: 20%, 0: 25%. It is known that the rates of contracting a certain disease according to blood groups are as follows: A: 7%, B: 6%, AB: 7%, 0: 4%. Accordingly, if a person selected by chance is known to have this disease, what is the probability of having blood group O?
16-(x²+x+2)²
Hola👋🏻 Toca en "Crear Nueva Tarea" para enviar tu problema de matemáticas. ¡Uno de nuestros expertos comenzará a trabajar en ello de inmediato!
t+72/t=-17
Question 3 A square has a perimeter given by the algebraic expression 24x – 16. Write the algebraic expression that represents one of its sides.
Construct a set of six pieces of data with​ mean, median, and midrange of 67 and where no two pieces of data are the same.